Journal ArticleDOI
Maximum Likelihood Estimates for a Multivariate Normal Distribution when Some Observations are Missing
TLDR
In this paper, the authors give an approach to derive maximum likelihood estimates of parameters of multivariate normal distributions in cases where some observations are missing (Edgett [2] and Lord [3], [4]).Abstract:
S EVERAL authors recently have derived maximum likelihood estimates of parameters of multivariate normal distributions in cases where some observations are missing (Edgett [2] and Lord [3], [4]). The purpose of this note is to give an approach to these problems that indicates the estimates with a minimum of mathematical manipulation; this approach can easily be applied to other cases. (The technique bears some resemblance to that of Cochran and Bliss in a dierent problem [1].) The method will be indicated by treating the simplest case involving a bivariate normal distribution. Suppose x and y have a bivariate normal distribution with means P, and m,u variances ,2 and UY2 and correlation coefficient p. We shall indicate the density by n(x, y|,ux, p,u; 2 a2; p). Suppose n observations are made on the pair (x, y) and N-n observations are made on x; that is, N-n observations on y are missing. The data areread more
Citations
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Journal ArticleDOI
Missing data: Our view of the state of the art.
Joseph L. Schafer,John W. Graham +1 more
TL;DR: 2 general approaches that come highly recommended: maximum likelihood (ML) and Bayesian multiple imputation (MI) are presented and may eventually extend the ML and MI methods that currently represent the state of the art.
Journal ArticleDOI
Inference and missing data
TL;DR: In this article, it was shown that ignoring the process that causes missing data when making sampling distribution inferences about the parameter of the data, θ, is generally appropriate if and only if the missing data are missing at random and the observed data are observed at random, and then such inferences are generally conditional on the observed pattern of missing data.
Journal ArticleDOI
A Test of Missing Completely at Random for Multivariate Data with Missing Values
TL;DR: In this article, the authors proposed a global test statistic for multivariate data with missing values, that is, whether the missing data are missing completely at random (MCAR), that is whether missingness depends on the variables in the data set.
Journal ArticleDOI
Inference and missing data
TL;DR: In this paper, it was shown that ignoring the process that causes missing data when making sampling distribution inferences about the parameter of the data, θ, is generally appropriate if and only if the missing data are missing at random and the observed data are observed at random, and then such inferences are generally conditional on the observed pattern of missing data.
Journal ArticleDOI
The Relative Performance of Full Information Maximum Likelihood Estimation for Missing Data in Structural Equation Models
TL;DR: A Monte Carlo simulation examined the performance of 4 missing data methods in structural equation models and found that full information maximum likelihood (FIML) estimation was superior across all conditions of the design.
References
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Journal ArticleDOI
Estimation of Parameters from Incomplete Data
TL;DR: In this article, the problem of estimating the parameters of a normal trivariate population from incomplete data is dealt with in a special case for which explicit solutions to the maximum likelihood equations are readily obtained.
Journal ArticleDOI
Multiple Regression with Missing Observations Among the Independent Variables
TL;DR: This data indicates that the ability of laser-spot assisted, 3D image analysis to characterize the geometry of the tear gas canister and its application in the battlefield is a viable process and should be investigated further.
Journal ArticleDOI
Discriminant Functions with Covariance
W. G. Cochran,C. I. Bliss +1 more
TL;DR: In this paper, the authors discuss the extension of the discriminant function to the case where certain variates (called the covariance variates) are known to have the same means in all populations.
Journal ArticleDOI
Equating test scores—A maximum likelihood solution
TL;DR: In this paper, a maximum likelihood solution is presented for the following special equating problem: two tests, U and V, are to be equated, making use of a third "anchor" test, W. The examinees are divided into two random halves.